Mathematical Genealogy of Pramod N. Achar

Ph.D., Universit¨at Leipzig, 1665–66 Otto Mencke Ex Theologia naturali—De Absoluta Dei Simplicitate, Micropolitiam, id est Rempubli- cam In Microcosmo Conspicuam

Ph.D., Universit¨at Leipzig, 1685 Johann Wichmannshausen Disputationem Moralem De Divortiis Secundum Jus Naturae

Dr. Phil., Martin-Luther-Universit¨atHalle-Wittenberg, 1713 Christian Hausen De corpore scissuris figurisque non cruetando ductu

Ph.D., Universit¨at Leipzig, 1739 Abraham K¨astner Theoria radicum in aequationibus

Georg Lichtenberg Dr. Phil., Georg-August-Universit¨atG¨ottingen, 1765 Unknown

Dr. Phil., Georg-August-Universit¨atG¨ottingen, 1786 Johann Pfaff Commentatio de ortibus et occasibus siderum apud auctores classicos commemoratis

Ph.D., Universit¨at Helmstedt, 1799 Carl Gauß Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse

Dr. Phil., Georg-August-Universit¨atG¨ottingen, 1800 Heinrich Brandes Unknown

Dr. Phil., Georg-August-Universit¨atG¨ottingen, 1810 Friedrich Bessel Unknown

Ph.D., Universit¨at Berlin, 1823 Heinrich Scherk De evolvenda functione . . . disquisitiones nonnullae analyticae

Ph.D., Martin-Luther-Universit¨atHalle-Wittenberg, 1831 Ernst Kummer De cosinuum et sinuum potestatibus secundum cosinus et sinus arcuum multiplicium evolvendis

Christoph Gudermann Ph.D., Georg-August-Universit¨atG¨ottingen, 1841 Uber¨ die Entwicklung der Modularfunctionen

Ph.D., Universit¨at K¨onigsberg, 1854 Karl Weierstraß Unknown

Ph.D., Universit¨at Berlin, 1864 Hermann Schwartz De superficiebus in planum explicabilibus primorum septem ordinum

Leopold Fej´er Ph.D., E¨otv¨osLor´andUniversity, 1902 Unknown

Ph.D., E¨otv¨osLor´andUniversity, 1912 Unknown

Ph.D., University, 1918 C. Some Problems Concerning Spherical Harmonics

Ph.D., , 1940 Ring Properties of Certain Classes of Functions

Ph.D., , 1954 Representations of a and its Enveloping Algebra on

Ph.D., Institute of Technology, 1976 Lie Algebra Cohomology and the Representations of Semisimple Lie Groups

Ph.D., Massachusetts Institute of Technology, 2001 Pramod Achar Equivariant Coherent Sheaves on the Nilpotent Cone for Complex Reductive Lie Groups